1. Field of the Invention
The present invention pertains to the field of controllers. More specifically, the present invention relates to controllers for ramping and stabilizing a plant at a setpoint.
2. Background Information
In control of a plant the control system attempts to ramp up and stabilize a particular variable under control to a setpoint. For many plants, linear controllers with integral action track constant setpoints asymptotically, i.e., the variable under control converges to a constant desired value. When the setpoint changes with a constant ramp rate however, linear controllers with integral action typically maintain a nonzero quasi-steady state ramping offset error.
FIG. 1 illustrates an example of a graph showing quasi-steady state offset error in a plant during ramping. Line 110 illustrates the ramping and stabilizing of the setpoint variable programmed by the user, r.sub.desired (t), to a final setpoint 140. However, when using a linear controller with integral action, the variable under control r.sub.actual (t) 130 maintains a quasi-steady state error 120 during ramping. In the example illustrated in FIG. 1, the difference between the variable under control r.sub.actual (t) and the setpoint variable programmed by the user r.sub.desired (t) has two components: a nonzero quasi-steady state offset error 150 and a zero steady-state error 160.
An example of a system exhibiting quasi-steady state offset may be a semiconductor furnace where the variable under control is the temperature of the furnace. The furnace is heated to a desired temperature (setpoint temperature) for a particular process. By using a linear controller with integral action, the actual furnace temperature converges to the desired constant setpoint asymptotically. During ramping, however, the furnace temperature lags the desired temperature by a nearly constant value (i.e., is offset).
There have been attempts to compensate for quasi-steady state offsets during ramping. One example is to increase the gain of the controller to a higher level during ramping and then decrease the gain to a lower level when the system is near the final setpoint. Increasing the feedback control gain typically reduces the size of the quasi-steady state offset during ramping. However, there are some limits to what higher gain can do for a system. When using higher gain, the system may bump into control actuator limits and reduce the performance of the controller. Additionally, a high gain controller may not always successfully stabilize the system being controlled. Further, higher gain increases the sensitivity of the system to noise (e.g., sensor and/or electrical noise). Increasing the noise sensitivity of the system and/or bumping into the control actuator may degrade the performance of the system and ultimately affect the product of the system under control.
In the semiconductor furnace example given above, the increased noise sensitivity or the limitations of the control actuator may make the control system unstable, or be unable to accurately maintain the setpoint temperature. Thus, the integrity of the process is sacrificed which may ultimately affect the reliability and performance of the semiconductor devices being manufactured.
Another attempt to compensate for quasi-steady state offset during ramping is to use feedforward control. One feedforward control method takes the ramping portion of the setpoint variable programmed by the user, r.sub.desired (t), and modifies it by the ramp offset error (i.e., the nonzero quasi-steady state offset error). In other words, the ramp offset error is added to the setpoint r.sub.desired (t) which compensates for the ramp offset error and brings the variable under control close to the original setpoint variable programmed by the user.
FIG. 2 illustrates an example of a graph showing feedforward compensation in a system during ramping. Line 210 illustrates the setpoint variable programmed by the user, r.sub.desired (t), to a final setpoint 240. By knowing the ramp rate offset 150 of the plant (illustrated in FIG. 1) the feedforward control mechanism modifies the portion of the setpoint variable 210 during ramping by advancing the setpoint an amount equivalent to the ramp rate offset 250 (i.e., the ramp rate offset 150 illustrated in FIG. 1) in order to bring the variable under control r.sub.actual (t) 220 of the system back to near the original setpoint variable programmed by the user 210. Line 220 illustrates the value of the variable under control during ramping of ramping using feedforward control. As shown in the example illustrated in FIG. 2, however, the feedforward method causes the setpoint to rise above the final setpoint 240 in a "spike" 270. This spike results in an overshoot 280 of the final setpoint 240. In many manufacturing control systems, an excessive overshoot of the final setpoint 240 of the system may affect the integrity of the system and ultimately affect the product of the system or results produced by the system.
FIG. 4 illustrates a block diagram of an example of a system 400 including feedforward control. System 400 includes plant 410 (i.e., the device under control), controller 420, and feedforward mechanism 430. The setpoint (r.sub.desired) 445 is input into the feedforward mechanism 430, which outputs a modified value of the variable under control, r.sub.feedforward 450, to the controller 420. Controller 420 in turn uses r.sub.feedforward 450 along with measurements to control the plant. The plant produces r.sub.actual (t) 460 which is the actual value of the variable under control that is realized in the plant 410.
As discussed above, the use of a feedforward system 400 may result in an overshoot of the variable under control as compared to the setpoint variable programmed by the user. In the semiconductor furnace example given above, the overshoot 280 may increase the temperature level of the furnace beyond the temperature desired. This increase may result in poor process results and may even damage the semiconductor wafers being processed. Thus, the integrity of the process is degraded which may ultimately affect the reliability and performance of the semiconductor device being manufactured.
What is needed is a method and system for ramp following and overshoot minimization.